"Skill Details
Veterinary works on all tamable creatures.
The complementary skill for Veterinary is Animal Lore, like Anatomy for Healing.
The amount of hitpoints healed is not a percentage but a range determined by your skill levels of the Veterinary Skill and Animal Lore. The formula is the same for Veterinary/Animal Lore and Healing/Anatomy.
The delay for healing a pet with the Veterinary skill is 2 seconds, regardless of a player's dexterity.
You need a minimum of
60.0 skill points in Animal Lore and Veterinary to be able to cure poison 80.0 skill points in Animal Lore and Veterinary to be able to resurrect a bonded pet.
Veterinary will always cure the poison first. In order to heal damage you have to apply another bandage. You can not heal a pet before it is cured.
Optimizing your gains
While the Veterinary skill itself is difficulty based, skill gain is not - you don't have to heal increasing amounts of damage or cure poison as your skill goes up in order to keep gaining. Attempt to apply as many bandages as possible, regardless of the amount of damage. Just avoid applying bandages to nearly undamaged pets, the message "you heal what little damage your patient had" tells you that it was not enough to get a chance at a gain.
Amount of Hitpoints Healed
Primarily, the amount of hitpoints healed is determined by your skilllevels in Veterinary and Animal lore, but you also get a small bonus which is derived from the total number of hitpoints of the pet you are attempting to heal. The formula to determine the amount of hitpoints healed is:
Min_Healed=(lore / 5) + (vet / 5) + 3
Max_Healed=(lore / 5) + (vet / 2) + 10
Amount Healed=random (Min_Healed, Max_Healed) + (pet's max HP / 100)
For more in-depth information consult the The UO Tamer Forum"

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